Combining machine learning with languages like ProLog?
In reference to your exact question there is published research that attempts to bring these two areas together.

“HolStep: A Machine Learning Dataset for Higher-order Logic Theorem Proving” by Cezary Kaliszyk, François Chollet, Christian Szegedy (2017) 
https://arxiv.org/abs/1703.00426

That group also has other published work related to the subject.

Regardless of their results they list several areas of logical systems that are highly suited to machine learning methods:

• Predicting whether a statement is useful in the proof of a given conjecture

• Predicting the dependencies of a proof statement (premise selection)

• Predicting whether a statement is an important one (human named)

• Predicting which conjecture a particular intermediate statement originates from

• Predicting the name given to a statement

• Generating intermediate statements useful in the proof of a given conjecture 

• Generating the conjecture the current proof will lead to

It’s tough to know whether or not you can combine Higher Order Logic and Machine Learning in an effective way without needing to create a general AI. This is equivalent to wondering if an effective merging of the two areas is an AI-complete / AI-hard problem.

There are active attempts at general AI by researchers such as Ben Goertzel (many others as well but just to give a popular name for googling). Research into general AI would give you an idea of whether or not other pieces of the puzzle are needed in order to create something “highly intelligent”.